Asian option as a fixed-point

Adriana Ocejo

Papers from arXiv.org

Abstract: We characterize the price of an Asian option, a financial contract, as a fixed-point of a non-linear operator. In recent years, there has been interest in incorporating changes of regime into the parameters describing the evolution of the underlying asset price, namely the interest rate and the volatility, to model sudden exogenous events in the economy. Asian options are particularly interesting because the payoff depends on the integrated asset price. We study the case of both floating- and fixed-strike Asian call options with arithmetic averaging when the asset follows a regime-switching geometric Brownian motion with coefficients that depend on a Markov chain. The typical approach to finding the value of a financial option is to solve an associated system of coupled partial differential equations. Alternatively, we propose an iterative procedure that converges to the value of this contract with geometric rate using a classical fixed-point theorem.

Date: 2015-10, Revised 2018-04
New Economics Papers: this item is included in nep-sea
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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:1510.08161

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